Frank Wilczek The Origin of Mass - MIT...recommend QED: The Strange Theory of Electrons and Light, byRichard Feynman. The basic concept of QED is the response of photons to electric

24 ) wilczek mit physics annual 2003

veryday work at the frontiers of modern

physics usually involves complex concepts and

extreme conditions. We speak of quantum fields, entan-

glement, or supersymmetry, and analyze the ridiculously small

or conceptualize the incomprehensibly large. Just as Willie

Sutton famously explained that he robbed banks because “that’s

where the money is,” so we do these things because “that’s where

the Unknown is.” It is an amazing and delightful fact, however,

that occasionally this sophisticated work gives answers to child-

like questions about familiar things. Here I’d like to describe

how myown work on subnuclear forces, the world of quarks and

gluons, casts brilliant new light on one such child-like question:

What is the origin of mass?

Frank Wilczek

E

The Origin of Mass

mit physics annual 2003 wilczek ( 25

Has Mass an Origin?That a question makes grammatical sense does not guarantee

that it is answerable, or even coherent.The concept of mass is one of the first things we discuss in my

freshman mechanics class. Classical mechanics is, literally, unthink-able without it. Newton’s second law of motion says that the acceler-

ation of a body is given by dividing the force acting upon it by its mass.So a bodywithout mass wouldn’t know how to move, because you’d be divid-

ing by zero. Also, in Newton’s law of gravity, the mass of an object governs thestrength of the force it exerts. One cannot build up an object that gravitates, out

of material that does not, so you can’t get rid of mass without getting rid of grav-ity. Finally, the most basic feature of mass in classical mechanics is that it isconserved. For example, when you bring together two bodies, the total mass is justthe sum of the individual masses. This assumption is so deeply ingrained that itwas not even explicitly formulated as a law. (Though I teach it as Newton’sZeroth Law.) Altogether, in the Newtonian framework it is difficult to imaginewhat would constitute an “origin of mass,’’ or even what this phrase could possi-bly mean. In that framework mass just is what it is—a primary concept.

Later developments in physics make the concept of mass seem less irreducible.Einstein’s famous equation of special relativity theory, written in that way,betrays the prejudice that we should express energy in terms of mass. But we can write the same equation in the alternative form . When expressed in this form, it suggests the possibility of explaining mass in terms of energy.Einstein was aware of this possibility from the beginning. Indeed, his original 1905paper is entitled, “Does the Inertia of a Body Depend on Its Energy Content?” andit derives not Einstein was thinking about fundamental physics,not bombs.

E=mc2.m=E/c2,

m=E/c2

E=mc2

At modern particle accelerators, comes to life.For example, in the Large Electron Positron collider (LEP),at the CERN laboratory near Geneva, beams of electrons andantielectrons (positrons) were accelerated to enormous ener-

gies. Powerful, specially designed magnetscontrolled the paths of the particles, and causedthem to circulate in opposite directions around abig storage ring. The paths of these beams inter-sected at a few interaction regions, where collisionscould occur. [After more than a decade of fruit-ful operation, in which MIT scientists played a lead-ing role, the LEP machine was dismantled in2000. It is making way for the Large HadronCollider (LHC), which will use the same tunnel.

LHC will collide protons instead of electrons, and will oper-ate at much higher energy. Hence the past tense.]

When a collision between a high-energy electron and ahigh-energy positron occurs, we often observe that many parti-cles emerge from the event. [See Figures 2a and 2b on page 29.]The total mass of these particles can be thousands of times themass of the original electron and positron. Thus mass has beencreated, physically, from energy.

m=E/c2


QED and QCD in Pictures(FIGURES 1A, 1B, 1C, AND 1D)

The physical content of quantum electrodynamics (QED)

is summarized in the algorithm that associates a probability

amplitude with each of its Feynman graphs, depicting a

possible process in space-time.The Feynman graphs are

constructed by linking together hubs, more conventionally

called interaction vertices, of the form shown in 1a.The solid

line depicts the world-line of an electrically charged particle,

and the squiggly line straddles the world-line of a photon. By

connecting hubs together we can describe physical processes

such as the interaction between electrons, as shown in 1b.

Quantum chromodynamics (QCD) can be summarized similarly,

but with a more elaborate set of ingredients and hubs.

There are three kinds of charges, called colors.

Quarks resemble electrons in their mechanical

properties (technically, they are spin-1⁄2 fermions),

but their interactions are quite different, because

they carry a unit of color charge. Quarks come in

several flavors— u, d, s, c, b, and t—so we have u u u

d d d and so forth. Only u and d, which have very

small masses, are important in ordinary matter.The

others are heavy and unstable. Gluons resemble

photons in their mechanical properties (technically,

they are massless spin-1 bosons), but their interac-

tions are quite different.There are eight different

types of color gluons, which respond to and

change the color charges of quarks they interact

with. A typical hub for a quark-gluon interaction

is shown in 1c, along with a hub for gluon-gluon

interaction.The latter has no analog in QED,

because the photon carries no electric charge.

Asymptotic freedom, and all the drastic differences

between how particles with and without color

charges are observed to behave, ultimately arise

from these new gluon-gluon interactions.

In principle we can try to use Feynman diagrams to

calculate the quark-quark interaction, as shown in

1d. But unlike in QED, in QCD contributions from

graphs containing many hubs are not small, and

this method is impractical.

)

1c 1d

1a 1b

+

Many Others

+


What Matters for MatterHaving convinced ourselves that the question of the origin of mass might makesense, let us now come to grips with it, in the very concrete form that it takes forordinary matter.

Ordinary matter is made from atoms. The mass of atoms is overwhelminglyconcentrated in their nuclei. The surrounding electrons are of course crucial fordiscussing how atoms interact with each other—and thus for chemistry, biology,and electronics. But they provide less than a part in a thousand of the mass!Nuclei, which provide the lion’s share of mass, are assembled from protons andneutrons. All this is a familiar, well-established story, dating back seventy yearsor more.

Newer and perhaps less familiar, but by now no less well-established, is the nextstep: protons and neutrons are made from quarks and gluons. So most of the massof matter can be traced, ultimately, back to quarks and gluons.

QCD: What It IsThe theoryof quarks and gluons is called quantum chromodynamics, or QCD. QCDis a generalization of quantum electrodynamics (QED). For a nice description ofquantum electrodynamics, written by an MIT grad who made good, I highlyrecommend QED: The Strange Theory of Electrons and Light, byRichard Feynman.

The basic concept of QED is the response of photons to electric charge. Figure 1a shows a space-time picture of this core process. Figure 1b shows howit can be used to describe the effect of one electric charge on another, through exchangeof a “virtual” photon. [A virtual photon is simply one that gets emitted andabsorbed without ever having a significant life of its own. So it is not a particle youcan observe directly, but it can have effects on things you do observe.] In other words,Figure 1b describes electric and magnetic forces!

Pictures like these, called Feynman diagrams, may look like childish scribbles,but their naïve appearance is misleading. Feynman diagrams are associated withdefinite mathematical rules that specify how likely it is for the process they depictto occur. The rules for complicated processes, perhaps involving many real andvirtual charged particles and many real and virtual photons, are built up in acompletely specific and definite way from the core process. It is like makingconstructions with TinkerToys®. The particles are different kind of sticks you canuse, and the core process provides the hubs that join them. Given these elements,the rules for construction are completely determined. In this way all the contentof Maxwell’s equations for radio waves and light, Schrödinger’s equation foratoms and chemistry, and Dirac’s more refined version including spin—all this,and more, is faithfully encoded in the squiggle [Figure 1a].

At this most primitive level QCD is a lot like QED, but bigger. The diagramslook similar, and the rules for evaluating them are similar, but there are more kinds of sticks and hubs. More precisely, while there is just one kind of charge inQED—namely, electric charge—QCD has three different kinds of charge. Theyare called colors, for no good reason. We could label them red, white, and blue;


or alternatively, if we want to make drawing easier, and to avoid the colors of theFrench flag, we can use red, green, and blue.

Every quark has one unit of one of the color charges. In addition, quarks comein different “flavors.”The onlyones that play a role in ordinary matter are two flavorscalled u and d, for up and down. [Of course, quark “flavors” have nothing to dowith how anything tastes. And, these names for u and d don’t imply that there’sany real connection between flavors and directions. Don’t blame me; when I getthe chance, I give particles dignified scientific-sounding names like axion and anyon.]There are u quarks with a unit of red charge, d quarks with a unit of greencharge, and so forth, for six different possibilities altogether.

And instead of one photon that responds to electric charge, QCD has eight colorgluons that can either respond to different color charges or change one into another.

So there is quite a large varietyof sticks, and there are also many different kindsof hubs that connect them. It seems like things could get terribly complicated andmessy. And so theywould, were it not for the overwhelming symmetryof the theory.If you interchange red with blue everywhere, for example, you must still get thesame rules. The more complete symmetry allows you to mix the colors continu-ously, forming blends, and the rules must come out the same for blends as for purecolors. I won’t be able to do justice to the mathematics here, of course. But the finalresult is noteworthy, and easy to convey: there is one and only one way to assignrules to all the possible hubs so that the theory comes out fully symmetric. Intri-cate it may be, but messy it is not!

With these understandings, QCD is faithfully encoded in squiggles like Figure 1c, and the force between quarks emerges from squiggles like Figure 1d. Wehave definite rules to predict how quarks and gluons behave and interact. The calcu-lations involved in describing specific processes, like the organization of quarks andgluons into protons, can be very difficult to carry through, but there is no ambiguityabout the outcome. The theory is either right or wrong—there’s nowhere to hide.

How We Know It’s RightExperiment is the ultimate arbiter of scientific truth. There are many experi-ments that test the basic principles of QCD. Most of them require rather sophis-ticated analysis, basically because we don’t get to see the underlying simple stuff,the individual quarks and gluons, directly. But there is one kind of experimentthat comes very close to doing this, and that is what I’d like to explain to you now.

I’ll be discussing what was observed at LEP. But before entering into details,I’d like to review a fundamental point about quantum mechanics, which is neces-sary background for making any sense at all of what happens. According to the principles of quantum mechanics, the result of an individual collision is unpredictable. We can, and do, control the energies and spins of the electrons andpositrons precisely, so that precisely the same kind of collision occurs repeatedly;nevertheless, different results emerge. By making many repetitions, we can deter-mine the probabilities for different outcomes. These probabilities encode basic information about the underlying fundamental interactions; according to quantum mechanics, they contain all the meaningful information.

Figures 2a and 2b: Real JetsThese are pictures of the results of electron-positron collisions at LEP, taken by the L3 collaboration led by Professors Ting,Becker, and Fisher.The alignment of energeticparticles in jets is visible to the naked eye.

Figures 2c and 2d: Conceptual JetsThese diagrams represent our conceptualmodel of the deep structure beneath jetproduction as it is observed. Electrons andpositrons annihilate into “pure energy”(a virtual photon, actually), whichmaterializes into a quark-antiquark pair.The quark and antiquark usually dressthemselves with soft radiation, as describedin the text, and we observe a two-jet event.About 10% of the time, however, a hardgluon is radiated.Then quark, antiquark,and gluon all dress themselves with soft

radiation, and we see threejets. Figures 2c and 2dhave been drawn toparallel the geometry ofthe observations shown inFigures 2a and 2b. (N.B.To keep things simple, Ihave not tried to maintainthe full color scheme fromFigure 1.)


When we examine the results of collisions at LEP, we find there are two broadclasses of outcomes. Each happens about half the time.

In one class, the final state consists of a particle and its antiparticle movingrapidly in opposite directions. These could be an electron and an antielectron

a muon and an antimuon or a tau and an antitau The littlesuperscripts denote signs of their electric charges, which are all of the sameabsolute magnitude. These particles, collectively called leptons, are all closelysimilar in their properties.

Leptons do not carry color charges, so their main interactions are with photons,and thus their behavior should be governed by the rules of QED.

This is reflected, first of all, in the simplicityof their final states. Once produced,any of these particles could—in the language of Feynman diagrams—attach aphoton using a QED hub, or alternatively, in physical terms, radiate a photon. Thebasic coupling of photons to a unit charge is fairly weak, however. Thereforeeach attachment is predicted to decrease the probability of the process beingdescribed, and so the most usual case is no attachment.

In fact, the final state , including a photon, does occur, with about 1%of the rate of simply (and similarly for the other leptons). By studying thee−e+

e−e+�

(�−�+).(�−�+),(e−e+),

2a

2b

2c

2d

Cour

tesy

L3 at

CERN

Cour

tesy

L3 a

tCER

N


details of these 3-particle events, such as the probability for the photon to be emit-ted in different directions (the “antenna pattern”) and with different energy, wecan check all aspects of our hypothesis for the underlying hub. This provides a wonder-fully direct and incisive way to check the soundness of the basic conceptual build-ing block from which we construct QED. We can then go on to address theextremely rare cases (.01%) where two photons get radiated, and so forth.

For future reference, let’s call this first class of outcomes “QED events.”The other broad class of outcomes contains an entirely different class of parti-

cles, and is in manyways far more complicated. In these events the final state typi-cally contains ten or more particles, selected from a menu of pions, rho mesons,

protons and antiprotons, and many more. These are all particlesthat in other circumstances interact stronglywith one another, andthey are all constructed from quarks and gluons. Here, they makea smorgasbord of Greek and Latin alphabet soup. It’s such a messthat physicists have pretty much given up on trying to describe allthe possibilities and their probabilities in detail.

Fortunately, however, some simple patterns emerge if we changeour focus from the individual particles to the overall flow of energyand momentum.

Most of the time—in about 90%of the cases—the particles emergeall moving in either one of two possible directions, opposite to oneanother. We say there are back-to-back jets. (Here, for once, the scien-

tific jargon is both vivid and appropriate.) About 9% of the time, we find flows inthree directions; about .9% of the time, four directions; and by then we’re left witha very small remainder of complicated events that are hard to analyze this way.

I’ll call the second broad class of outcomes “QCD events.” Representative 2-jet and 3-jet QCD events, as they are actuallyobserved, are displayed in Figure 2.

Now if you squint a little, you will find that the QED events and the QCD eventsbegin to look quite similar. Indeed, the pattern of energy flow is qualitatively thesame in both cases, that is, heavily concentrated in a few narrow jets. There aretwo main differences. One, relatively trivial, is that multiple jets are more commonin QCD than in QED. The other is much more profound. It is that, of course, inthe QED events the jets are just single particles, while in the QCD events the jetsare sprays of several particles.

In 1973, while I was a graduate student working with David Gross at Prince-ton, I discovered the explanation of these phenomena. We took the attitude that the deep similarities between the observed basic behaviors of leptons (basedon QED) and the strongly interacting particles might indicate that the stronglyinteracting particles are also ultimately described by a simple, rule-based theory,with sticks and hubs. In other words, we squinted.

To bring our simplified picture of the QCD events into harmonywith the obser-vations, we relied on a theoretical discovery I’ll describe momentarily, which wechristened asymptotic freedom. (Please notice that our term is not “cute.”) Actu-ally, our discoveryof asymptotic freedom preceded these specific experiments, so

“It’s such a mess that

physicists have pretty much

given up on trying to describe

all the possibilities and their

probabilities in detail.”


we were able to predict the results of these experiments before theywere performed.As a historical matter, we discovered QCD and asymptotic freedom by trying tocome to terms with the MIT-SLAC “scaling” experiments done at the StanfordLinear Collider in the late 1960s, for which Jerome Friedman, Henry Kendall, andRichard Taylor won the Nobel Prize in 1990. Since our analysis of the scaling exper-iments using QCD was (necessarily) more complicated and indirect, I’ve chosento focus here on the later, but simpler to understand, experiments involving jets.

The basic concept of asymptotic freedom is that the probability for a fast-moving quark or gluon to radiate away some of its energy in the form of other quarksand gluons depends on whether this radiation is “hard”or “soft”. Hard radiationis radiation that involves a substantial deflection of the particle doing the radiat-ing, while soft radiation is radiation that does not cause such a deflection. Thushard radiation changes the flow of energy and momentum, while soft radiationmerely distributes it among additional particles, all moving together. Asymptoticfreedom says that hard radiation is rare, but soft radiation is common.

This distinction explains why on the one hand there are jets, and on the otherhand why the jets are not single particles. A QCD event begins as the material-ization of quark and antiquark, similar to how a QED event begins as the mate-rialization of lepton-antilepton. They usually give us two jets, aligned along theoriginal directions of the quark and antiquark, because only hard radiation canchange the overall flow of energy and momentum signifi-cantly, and asymptotic freedom tells us hard radiation is rare.When a hard radiation does occur, we have an extra jet! Butwe don’t see the original quarks or antiquarks, individually,because they are always accompanied by their soft radiation,which is common.

By studying the antenna patterns of the multi-jet QCDevents we can check all aspects of our hypotheses for the under-lying hubs. Just as for QED, such antenna patterns providea wonderfully direct and incisive way to check the sound-ness of the basic conceptual building blocks from which weconstruct QCD.

Through analysis of this and many other applications,physicists have acquired complete confidence in the funda-mental correctness of QCD. By now experimenters use itroutinely to design experiments searching for new phenomena, and they refer towhat they’re doing as “calculating backgrounds” rather than “testing QCD”!

Many challenges remain, however, to make full use of the theory. The difficultyis always with the soft radiation. Such radiation is emitted veryeasily, and that makesit difficult to keep track of. You get a vast number of Feynman graphs, each withmany attachments, and they get more and more difficult to enumerate, let alonecalculate. That’s very unfortunate, because when we try to assemble a proton fromquarks and gluons none of them can be moving veryfast for verylong (they’re supposedto be inside the proton, after all), so all their interactions involve soft radiation.

“Just as for QED, such antenna

patterns provide a wonderfully

direct and incisive way to check

the soundness of the basic

conceptual building blocks from

which we construct QCD.”

To meet this challenge, a radically different strategy isrequired. Instead of calculating the paths of quarks and gluonsthrough space and time, using Feynman graphs, we let eachsegment of space-time keep track of how manyquarks and gluons

it contains. We then treat these segments as anassembly of interacting subsystems.

Actually in this context “we”means a collec-tion of hard-working CPUs. Skillfullyorches-trated, and working full time at teraflop speeds,they manage to produce quite a good accountof the masses of protons and other strongly inter-acting particles, as you can see from Figure 3.The equations of QCD, which we discoveredand proved from very different considera-tions, survive this extremely intense usagequite well. There’s a big worldwide effort, atthe frontiers of computer technology andhuman ingenuity, to do calculations like thismore accurately, and to calculate more things.

The Ingredients of QCD, Lite andFull-BodiedWith the answer in hand, let’s examine whatwe’ve got. For our purposes it’s instructive tocompare two versions of QCD, an idealized

version I call QCD Lite, and the realistic Full-Bodied version.QCD Lite is cooked up from massless gluons, massless u and

d quarks, and nothing else. (Now you can fully appreciate thewit of the name.) If we use this idealization as the basis for ourcalculation, we get the proton mass low by about 10%.

Full-Bodied QCD differs from QCD Lite in two ways. First,it contains four additional flavors of quarks. These do notappear directly in the proton, but they do have some effect as

virtual particles. Second, it allows for non-zero masses of the u and d quarks. The realistic value of these masses, though, turns out to be small, just a fewpercent of the proton mass. Each of these corrections changes the predicted massof the proton by about 5%, as we pass from QCD Lite to Full-Bodied QCD. Sowe find that 90% of the proton (and neutron) mass, and therefore 90% of the massof ordinary matter, emerges from an idealized theory whose ingredients areentirely massless.

The Origin of (most) MassNow I’ve shown you the theory that describes quarks and gluons, and thereforehas to account for most of the mass of matter. I’ve described some of the experiments


Its from Bits (FIGURE 3)

This plot, taken from the CP-PACS collaboration, shows a

comparison between the predictions of QCD and the masses

of particles.The green level lines indicate observed values of

particle masses, while the circles within intervals indicate

computational results and their statistical uncertainties.The K

meson is the left-most entry, while the proton and neutron are

N.The calculations employ cutting-edge computer technology

with massive parallelism, and even then some approximations

must be introduced to make the computations feasible.These

results are a remarkable embodiment of the vision that

elements of reality can be reproduced by purely conceptual

constructions—“Its from Bits”—because the underlying theory,

based on profoundly symmetrical equations, contains very few

adjustable parameters.

)

CP-PACS (1998)

GF11 (1993)

experiment

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

mhad[GeV]

�

[I]

�

�

[I]

��

�

quenched QCD

© Ce

nter

for C

ompu

tatio

nal P

hysic

s,Univ

ersit

y of T

suku

ba


that confirm the theory. And I’ve displayed successful calculations of hadron masses,including the masses of protons and neutrons, using this theory.

In a sense, these calculations settle the question. They tell us the origin of(most) mass. But simply having a computer spit out the answer, after gigantic andtotallyopaque calculations, does not satisfyour hunger for understanding. It is partic-ularly unsatisfactory in the present case, because the answer appears to be miracu-lous. The computers construct for us massive particles using building blocks—quarksand gluons—that are themselves massless. The equations of QCD Lite output Masswithout Mass, which sounds suspiciously like Something for Nothing. How didit happen?

The key, again, is asymptotic freedom. Previously, I discussed this phenome-non in terms of hard and soft radiation. Hard radiation is rare, soft radiation iscommon. There’s another wayof looking at it, mathematically equivalent, that isuseful here. From the classical equations of QCD, one would expect a force fieldbetween quarks that falls off as the square of the distance, as in ordinary electro-magnetism (Coulomb’s law). Its enhanced coupling to soft radiation, however, meansthat when quantum mechanics is taken into account a “bare”color charge, insertedinto empty space, will start to surround itself with a cloud of virtual color gluons.These color gluons fields themselves carry color charge, so they are sources of addi-tional soft radiation. The result is a self-catalyzing enhancement that leads to runawaygrowth. A small color charge, in isolation, builds up abig color thundercloud.

All this structure costs energy, and theoreticallythe energyfor a quark in isolation is infinite. That’s whywe never seeindividual quarks. Having only a finite amount of energyto work with, Nature always finds a way to short-circuitthe ultimate thundercloud.

One way is to bring in an antiquark. If the antiquarkcould be placed right on top of the quark, their colorcharges would exactly cancel, and the thundercloud wouldnever get started. There’s also another more subtle way tocancel the color charge by bringing together three quarks,one of each color.

In practice these exact cancellations can’t quite happen, however, becausethere’s a competing effect. Quarks obey the rules of quantum mechanics. It is wrongto think of them simply as tiny particles, rather they are quantum-mechanical wavi-cles. They are subject, in particular, to Heisenberg’s uncertainty principle, whichimplies that if you try to pin down their position too precisely, their momentumwill be wildly uncertain. To support the possibility of large momentum, theymust acquire large energy. In other words, it takes work to pin quarks down. Wavi-cles want to spread out.

So there’s a competition between two effects. To cancel the color chargecompletely, we’d like to put the quark and antiquark at precisely the same place;but they resist localization, so it’s costly to do that.

“But simply having a computer

spit out the answer, after

gigantic and totally opaque

calculations, does not satisfy

our hunger for understanding.”


This competition can result in a number of compromise solutions, where the quark and antiquark (or three quarks) are brought close together, but are notperfectly coincident. Their distribution is described by quantum mechanical wavefunctions. Many different stable wave-patterns are possible, and each correspondsto a different kind of particle that you can observe. There are patterns for protons,neutrons, and for each entry in the whole Greek and Latin smorgasbord. Each patternhas some characteristic energy, because the color fields are not entirely cancelledparticles and because the wavicles are somewhat localized. And that, through is the origin of mass.

A similar mechanism, though much simpler, works in atoms. Negativelycharged electrons feel an attractive electric force from the positively charged

nucleus, and from that point of view they’d like to snuggle righton top of it. Electrons are wavicles, though, and that inhibitsthem. The result, again, is a series of possible compromise solu-tions. These are what we observe as the energy levels of theatom. When I give the talk on which this article is based, atthis point I use Dean Dauger’s marvelous “Atom in a Box”program to show the lovely, almost sensuous patterns ofundulating waves that describe the possible states of thatsimplest of atoms, hydrogen. I hope you will explore “Atomin a Box”for yourself. You can link to it at http://www.dauger.com.In its absence, I will substitute a classic metaphor.

The wave patterns that describe protons, neutrons, and their relatives resem-ble the vibration patterns of musical instruments. In fact the mathematical equa-tions that govern these superficially very different realms are quite similar.

Musical analogies go back to the prehistory of science. Pythagoras, partlyinspired by his discovery that harmonious notes are sounded by strings whose lengthsare in simple numerical ratios, proposed that “All things are Number.”Kepler spokeof the music of the spheres, and his longing to find their hidden harmoniessustained him through years of tedious calculations and failed guesses before heidentified the true patterns of planetary motions.

Einstein, when he learned of Bohr’s atomic model, called it “the highest formof musicality in the sphere of thought.” Yet Bohr’s model, wonderful as it is,appears to us now as a very watered-down version of the true wave-mechanicalatom; and the wave-mechanical proton is more intricate and symmetric by far!

I hope that some artist/nerd will rise to the challenge, and construct a “Protonin a Box” for us to play with and admire.

The World as Concept, Algorithm, and NumberI will conclude with a few words concerning the broader significance of these devel-opments for our picture of the world.

A major goal of theoretical physics is to describe the world with the greatestpossible economyof concepts. For that reason alone, it is an important result thatwe can largely eliminate mass as an independent property that we are forced to

m=E/c2,

“The wave patterns that describe

protons, neutrons, and their

relatives resemble the vibration

patterns of musical instruments.”


introduce in order to describe matter accurately. But thereis more. The equations that describe the behavior of elemen-tary particles become fundamentally simpler and moresymmetric when the mass of the particles is zero. So elim-inating mass enables us to bring more symmetryinto the math-ematical description of Nature.

The understanding of the origin of mass that I’ve sketchedfor you here is the most perfect realization we have ofPythagoras’ inspiring vision that the world can be built upfrom concepts, algorithms, and numbers. Mass, a seemingly irreducible propertyof matter, and a byword for its resistance to change and sluggishness, turns outto reflect a harmonious interplayof symmetry, uncertainty, and energy. Using theseconcepts, and the algorithms they suggest, pure computation outputs the numer-ical values of the masses of particles we observe.

Still, as I’ve already mentioned, our understanding of the origin of mass is byno means complete. We have achieved a beautiful and profound understandingof the origin of most of the mass of ordinary matter, but not of all of it. The valueof the electron mass, in particular, remains deeplymysterious even in our most advancedspeculations about unification and string theory. And ordinarymatter, we have recentlylearned, supplies only a small fraction of mass in the Universe as a whole. Morebeautiful and profound revelations surely await discovery. We continue to searchfor concepts and theories that will allow us to understand the origin of mass in allits forms, by unveiling more of Nature’s hidden symmetries.

frank wilczek is considered one of the world’s most eminent theoretical physicists. He is known, among other things, for the discovery of asymptotic freedom, the development ofquantum chromodynamics, the invention of axions, and the discovery and exploitation of new forms of quantum statistics (anyons). When only 21 years old and a graduate student atPrinceton University, in work with David Gross he defined the properties of color gluons, which hold atomic nuclei together. Presently his main obsessions are exotic superfluidities onthe one hand and dark energy on the other. He suspects the two are connected.

Professor Wilczek received his B.S. degree from the University of Chicago and his Ph.D.from Princeton University. He taught at Princeton from 1974 to 1981. During the period 1981 to 1988, he was the Chancellor Robert Huttenback Professor of Physics at the University of California at Santa Barbara, and the first permanent member of the National ScienceFoundation’s Institute for Theoretical Physics. In the fall of 2000, he moved from the Institutefor Advanced Study, where he was the J.R. Oppenheimer Professor, to the MassachusettsInstitute of Technology, where he is the Herman Feshbach Professor of Physics. He has been aSloan Foundation Fellow (1975–77) and a MacArthur Foundation Fellow (1982–87). He hasreceived UNESCO’s Dirac Medal, the American Physical Society’s Sakurai Prize, the MichelsonPrize from Case Western University, and the Lorentz Medal of the Netherlands Academy for hiscontributions to the development of theoretical physics, and the Lilienfeld Prize for his writing.

He is a member of the National Academy of Sciences, the Netherlands Academy of Sciences,and the American Academy of Arts and Sciences. He is a Trustee of the University of Chicago,and an official advisor to CERN and to Daedalus. He contributes regularly to Physics Todayand to Nature, explaining topics at the frontiers of physics to wider scientific audiences.

“Eliminating mass enables us

to bring more symmetry into

the mathematical description

of Nature.”

Documents

Frank Wilczek The Origin of Mass - MIT...recommend QED: The Strange Theory of Electrons and Light, byRichard Feynman. The basic concept of QED is the response of photons to electric